Question: Solve for $x$ and $y$ using elimination. ${-2x+5y = 4}$ ${3x+4y = 40}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $5$ ${8x-20y = -16}$ $15x+20y = 200$ Add the top and bottom equations together. $23x = 184$ $\dfrac{23x}{{23}} = \dfrac{184}{{23}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-2x+5y = 4}\thinspace$ to find $y$ ${-2}{(8)}{ + 5y = 4}$ $-16+5y = 4$ $-16{+16} + 5y = 4{+16}$ $5y = 20$ $\dfrac{5y}{{5}} = \dfrac{20}{{5}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {3x+4y = 40}\thinspace$ and get the same answer for $y$ : ${3}{(8)}{ + 4y = 40}$ ${y = 4}$